That was the only time you noticed the speed boost the 4S felt no quicker and I expect the 5S to be the same.

I've had a 3G, 3GS, 4, and 4S and I can tell you each one IS much quicker at everything, from booting up to loading apps etc.
Think I timed my old 4 and my 4S booting up and the S was a whole 20 seconds quicker. Which is massive really.

I've had a 3G, 3GS, 4, and 4S and I can tell you each one IS much quicker at everything, from booting up to loading apps etc.
Think I timed my old 4 and my 4S booting up and the S was a whole 20 seconds quicker. Which is massive really.

I did that as well when i had my 4S and the missus had her 4. The 4S was a fraction quicker. Not 20 seconds though!

Also doing most things like browsing, opening apps, the 4S wasn't much faster. Games, there wasn't much i played the Mrs couldn't either.

I've had a 3G, 3GS, 4, and 4S and I can tell you each one IS much quicker at everything, from booting up to loading apps etc.
Think I timed my old 4 and my 4S booting up and the S was a whole 20 seconds quicker. Which is massive really.

I guess it depends on the apps but when I tested the 4 and 4S side by side there was hardly any difference in speed.In fact the 4 was slightly quicker at opening some apps.
The speed difference from 3 to 3G was was far more noticeable.

I think you may be confusing wake from sleep with boot up. I've just rebooted a friend's 4S and it took 38 seconds. My own iPhone 5 takes 30 seconds (but that may be because I am running Beta software).